What is probability in statistics?
The likelihood that an event will occur, expressed as a number between 0 and 1.
What is a sample space?
The set of all possible outcomes of a chance experiment. Example: rolling a die → {1,2,3,4,5,6}.
What is an event?
A collection of outcomes from the sample space. Example: rolling an even number → {2,4,6}.
What is a simple event?
An event that consists of only one possible outcome.
What are mutually exclusive events?
Events that cannot happen at the same time. Example: rolling a 2 and a 5 on one die roll.
What is the probability of any event A?
It is calculated as P(A) = number of favorable outcomes / total number of outcomes.
What are the basic rules of probability?
- 0 ≤ P(A) ≤ 1; 2. P(A) + P(not A) = 1; 3. For disjoint events, P(A or B) = P(A) + P(B).
What is the addition rule for non-mutually exclusive events?
P(A or B) = P(A) + P(B) - P(A and B).
What is conditional probability?
The probability of event A occurring given that event B has already occurred. P(A|B) = P(A and B) / P(B).
What are independent events?
Events where the occurrence of one does not affect the other. For independent events, P(A and B) = P(A) × P(B).
What are dependent events?
Events where one outcome influences the other. Example: drawing cards without replacement.
How are Venn diagrams used in probability?
They visually represent relationships between events such as overlap, union, or intersection.
